A Framework on Moment Model Reduction for Kinetic Equation

Through a deep investigation on the structure of the coefficient matrix of the globally hyperbolic regularized moment equations for the Boltzmann equation in [Z. Cai, Y. Fan, and R. Li, Commun. Math. Sci., 11 (2013), pp. 547--571], we propose a uniform framework for the derivation of reduced models from general kinetic equations. The resulting model appears as a symmetric hyperbolic moment system. This reveals the underlying reason why some models in the literature are hyperbolic while others are not. This framework provides a simple flow chart, following which a number of existing models can be derived in a new way. The framework is also helpful in discovering new models. We apply this to Grad's 13-moment distribution function and obtain a new 13-moment model with global hyperbolicity.